Common digital printer technology, such as that noted, for example in the Xerox DocuTech Printing System, reproduce variations in gray density by printing larger and smaller numbers of spots or pixels within a unit area. The decision to print a spot within a unit area is based upon a comparison of the required shade of gray with one of a set of predetermined threshold levels. If the gray is darker than a given threshold level, a spot is printed. If the gray is not as dark as a given threshold level, a spot is not printed. A set of thresholds, hereinafter referred to as a halftone cell or dot, include a plurality of different values against which comparisons can be made. The halftoning process is described in more detail in U.S. Pat. No. 4,149,194 to Holladay.
To print an image using a given halftone dot, the dot must be calibrated for a particular or target printer. Calibration refers to setting the threshold values of the halftone cell so that a given input gray is well represented by the printed image. Currently, this calibration is a slow and laborious process that has to be repeated for every halftone dot that one wants to use. The calibration will remain valid as long as the printer characteristics do not change. Because of the large effort required to calibrate a given halftone dot, the creation and use of new halftone dots is difficult and therefore seldom done. However, it is well understood that desirable effects and improved printing results can be obtained by using different dots in the image. Also different printers will have different calibrations for the same halftone dot, making it unfeasible to prepare halftoned images to be printed remotely with guaranteed tone reproduction.
The same calibration difficulty applies to other gray reproduction schemes or halftoning algorithms which are adaptive and do not use a set of fixed thresholds, such as error diffusion, pulse density modulation, and least squares model-based halftoning. This difficulty also applies to specialized bitmap patterns, sometimes generated from special halftone dots, called tint dots. These specialized bitmap patterns are used to represent uniform gray patches with periodic or quasi-periodic arrangements of binary pixels that give the illusion of a gray region. In all of these cases, the problem is to calibrate the printed patterns in a manner in which they give a visual impression of the proper gray level from the input gray image that they are supposed to represent.
See also, R. Floyd and L. Steinberg, "An adaptive algorithm for spatial grey scale," Proc. SID, Vol. 17/2, 1976 pp. 75-77, and T. Pappas, C-K. Dong and D. Neuhoff, "Measurement of printer parameter for model-based halftoning," J. Elect. Img., Vol. 2/3, 1993, pp. 193-204, and C. Rosenberg, "Measurement-based evaluation of a printer dot model for halftone algorithm tone correction," J. Elect. Img., Vol. 2/3, 1993, pp. 205-212.
The effects of light scattering in paper can be found in, Clapper et al., "The Effect of Multiple Internal Reflections on the Densities of Half-Tone Prints on Paper" Jnl. Opt. Soc. of Am., Vol 43, No. 7, 1953, pp. 600-603. Also, Ruckdeschel et al. "Yule-Nielsen Effect in Printing: a physical analysis", Applied Optics, Vol. 17, No. 21, November, 1978 pp. 3376-3383.